Senate Republicans huddled on Tuesday afternoon to get back on the same page: Attack Obamacare, not one another.

The regrouping came during a closed-door session amid a high-stakes Republican fissure over strategy on how to fight the president’s health care law and keep the government open.

“We’re talking about we can get back in a position where we’re talking about how harmful Obamacare [is] instead of disagreeing over tactics,” Sen. Ron Johnson (R-Wis.).

Sen. Ted Cruz of Texas and Sen. Mike Lee of Utah want Republicans to oppose ending debate on a House-passed spending bill later this week before Senate Majority Leader Harry Reid can strip out the defunding component, a tactic opposed by Senate Minority Leader Mitch McConnell (R-Ky.), Minority Whip John Cornyn (R-Texas) and Conference Vice Chairman Roy Blunt (R-Mo.). The leaders say they won’t vote procedurally against a bill that they support because it defunds Obamacare.

Given those differences, Republicans want to put the intraparty squabbles behind them and put the heat back on Democrats to defend Obamacare from GOP rhetorical attacks, which will be myriad as long as the spending bill is under Senate consideration.

“I don’t know how the Democrats defend the fact that businesses don’t have to comply but individuals do so I think the House strategy gets better as the week goes on,” Blunt said, predicting a “less divisive” party strategy as the week goes on.

Several Republicans have suggested the procedural focus should also be shifted back to Reid if the debate drags into the weekend. Reid plans to allow an amendment to strip out the Obamacare defunding provision, but the GOP wants to argue for amendments of their own to the bill.

“I suspect there will be utilization of all the time to talk about whether we get amendments, what those amendments are, are they good amendments,” said Sen. Saxby Chambliss (R-Ga.). “We have to change the dynamics.”

Sens. John McCain (R-Ariz.) and Lindsey Graham (R-S.C.) are pushing for a vote on the repeal of the medical device tax.

“We should have amendments, we should have some votes germane to Obamacare. I think [Reid] should allow us to have some votes,” Graham said.

Republicans are also discussing allowing a short-term spending bill to move quickly through the chamber to give the House more time to consider their options as Congress approaches an Oct. 1 government shutdown deadline.

“There certainly was a lot of discussion about giving back time on the motion to proceed so that possibly the House wouldn’t be jammed and would have time think about what they might send back,” said Sen. Bob Corker of Tennessee. “Everybody has to agree to that. You have to have 100 percent agreement even on the Democrat side. Democrats may decide it’s in their best interest to delay this so the House is jammed.”

But after lunching on Tuesday, the Senate GOP hadn’t yet settled on whether they will help speed the bill back to the House.

“I didn’t feel a sense for that happening,” Chambliss said.

Still, McConnell said he would not object if senators wanted to send the spending bill more quickly back to the House.

“If the House doesn’t get what we send over there until Monday, they’re in a pretty tough spot,” McConnell told reporters Tuesday. “And my own view is, the House having passed a bill that I really like … I‘d hate to put them in a tough spot.”

Yielding back that time would be at odds with the message from GOP Sen. Ted Cruz of Texas, who has vowed to use all of the Senate’s procedural tools to try to block Majority Leader Harry Reid from stripping out Obamacare funding later this week. That could mean stretching the Senate consideration of the bill all the way until Sunday, giving the House just hours to figure out its next move.

If House Speaker John Boehner (R-Ohio), Majority Leader Eric Cantor (R-Va.) and Majority Whip Kevin McCarthy (R-Calif.) got their hands on the Senate’s funding bill with a few days on the clock — as opposed to a few hours — they’d be much more likely to send it back to Reid’s chamber with another piece of Republican policy attached, according to several senior Republican aides. It would broaden Republicans’ options, one GOP source said, and give the party more time to count votes and maneuver.

Reid said if Senate Republicans want to speed up the process, it was “fine.” But he warned that if House Republicans changed the funding measure to send it back to the Senate, it would be a “sure-fire way to shut down the government.”

The tentative plan within Republican leadership as of Tuesday morning is to pass a debt ceiling bill Friday or Saturday, and then take up the continuing resolution when it comes back from the Senate. If the House gets the Senate funding bill earlier, House Republican leadership might have to accelerate its debt ceiling legislation, hardly an easy task in a chamber where raising the borrowing limit is seen as sacrilege.

Senate leaders have also settled on sending the House back a continuing resolution that expires on Nov. 15 rather than Dec. 15 as sent over the House last week. This approach would give Senate appropriators an attempt to rework the country’s spending program but risks another shutdown showdown. Reid confirmed the move during a news conference on Tuesday afternoon, saying it will “provide a greater opportunity for appropriations bills to pass the Senate.”

“If you go on a CR in December, you’re just on auto pilot and you’ve accepted sequester as the new normal. I reject both of those concepts,” said Senate Appropriations Chairwoman Barbara Mikulski (D-Md.)

Seung Min Kim, Jake Sherman and David Rogers contributed to this report.